GIS Based Studies in the Humanities and Social Sciences - Chpater 17 doc

Evaluation of School Redistricting by the School Family System 247factor in location planning; the average distance from home to school should be as small as possible.. Once spatial-opti

Trang 1

17

Evaluation of School Redistricting

by the School Family System

Yukio Sadahiro, Takashi Tominaga, and Saiko Sadahiro

CONTENTS

17.1 Introduction 244

17.2 Potential of GIS in Educational-Administration Research 244

17.2.1 GIS for Analysis in Educational-Administration Research 244

17.2.2 GIS for Planning in Educational-Administration Research246 17.2.3 GIS for Evaluation in Educational-Administration Research 247

17.3 GIS for School Redistricting 248

17.3.1 School Districting in Elementary and Lower-Secondary Education 248

17.3.2 School Redistricting in Elementary and Lower-Secondary Education 249

17.3.3 School-Family System 249

17.3.4 School Redistricting as a Spatial-Optimization Problem 250

17.4 School Redistricting in Kita Ward, Tokyo 251

17.4.1 Formulation of School-Redistricting Problem in Kita Ward, Tokyo 252

17.4.2 School Redistricting Where the Average Distance from Home to School Is the Objective Function 256

17.4.3 School Redistricting Where the Number of Students Assigned to Different Schools Is the Objective Function 259

17.5 Conclusion 262

References 262 2713_C017.fm Page 243 Thursday, September 22, 2005 9:07 AM

Trang 2

244 GIS-based Studies in the Humanities and Social Sciences

17.1 Introduction

Geographical Information System(GIS)is a set of tools for analyzing spatialobjects and phenomena interactively in a computer environment Since ittreats geographical information, it is effective in educational administration

to discuss geographical factors For instance, we can visualize the location

of schools, traffic networks, and public facilities as an integrated map Amap of schools and population distribution classified by ethnicity and race

is useful for discussing the educational program desirable in each school.Calculating the average distance from home to school, we can evaluate aphysical aspect of educational environment

This paper aims to present potentials of GIS in educational administration.Potential applications of GIS in educational administration are threefold:analysis, planning, and evaluation We discuss these subjects in turn in thefollowing sections We then show a methodology for treating school redis-tricting in GIS with a focus on the school-family system, a new concept inschool cooperation Applying the method to a concrete example of schoolredistricting in Tokyo, Japan, we will show the effectiveness of GIS in edu-cational administration In the last section, we summarize the conclusions

17.2 Potential of GIS in Educational-Administration Research

17.2.1 GIS for Analysis in Educational-Administration Research

One typical usage of GIS in educational administration is spatial analysis ofthe present status of education in a region Spatial analysis usually startswith visual analysis, which is followed by statistical and mathematical anal-ysis These steps are explained successively in the following

Visual analysis is an initial examination of spatial phenomena in GIS(MacEachren and Taylor, 1994; Nielson et al., 1997; Slocum, 1998; Gahegan,2000) Suppose, for instance, a map showing the location of schools, thenumber of students, and the population distribution of Hispanics (Figure17.1a) A spatial variation exists in the number of students among school.Some schools have very few students, while others have so many studentsthat they may be beyond their capacity Since a strong correlation existsbetween the number of students and that of Hispanics, we suppose that asudden increase of Hispanic students may have caused lack of schools, whichhas lowered the quality of educational environment

If our interest lies in the regional variation in the grade of students, wemay overlay a map of students with their grade on the map showing pop-

2713_C017.fm Page 244 Thursday, September 22, 2005 9:07 AM

Trang 3

Evaluation of School Redistricting by the School Family System 245

ulation distribution classified by gender, age, ethnicity, and race The quality

of teachers and educational programs can also be visualized as attributes ofschools to be discussed in relation to regional variation of students

Visual analysis is also useful for assessing educational environment in aregion A map indicating the location of schools and individual students isuseful for assessing the regional variance in the distance from home toschool Overlaying the maps of traffic networks and topography, we canevaluate the time distance instead of physical distance Maps showing crimeoccurrences and land-use patterns may also work as indicators of educa-tional environment (Figure 17.1b) Though we can do these analyses manu-ally using paper maps, GIS drastically improves the efficiency and accuracy

Trang 4

resources, both human and physical, and so forth They are calculated forindividual schools, reported by the histogram, mean, variance, the maximumand minimum values, and often represented by the size of map symbols inGIS

These descriptive measures are useful for generating research hypotheses

To test research hypotheses, statistical tests are performed In addition totraditional statistics, spatial statistics are often used in GIS (Isaaks and Srivas-tava, 1989; Cressie, 1993; Diggle, 2003) Spatial statistics are a subfield ofstatistics focusing on the spatial distribution of stochastic phenomena.Whether or not the students of high grades are clustered in specific regionscan be statistically tested at a given significance level Spatial relationshipbetween the location of schools and juvenile offenses can also be statisticallyevaluated

Once a hypothesis is statistically supported, mathematical models are built

to represent spatial phenomena General spatial models include regression models (Bailey and Gatrell, 1995; Fotheringham et al., 2002), geo-statistics, spatial-point processes (Stoyan and Stoyan, 1994; Diggle, 2003),spatial econometrics (Anselin, 1988; Anselin and Florax, 1995), and spatial-choice models (Ben-Akiva and Lerman, 1985; Fischer et al., 1990; Smith andSen, 1995) These models describe spatial phenomena in a formal mannerusing mathematical and statistical theories Suppose, for instance, schoolchoice of students, a kind of spatial choice behavior Various factors areconsidered to affect school choice; the distance from home to school, thequality of education and facilities, the environment around school, and soforth To measure the weight of each factor in school choice, a discrete choicemodel is often utilized Collecting the data of school choice, we can estimatethe model and evaluate quantitatively the degree of influence of each factor.This helps us in understanding one aspect of human behavior in education

spatial-17.2.2 GIS for Planning in Educational-Administration Research

In educational administration, analysis is usually followed by plan making.For example, if the quality of education varies considerably among schools,

a plan may have to be devised that assures all the schools of a certain quality

of education GIS can be utilized at this stage, that is, GIS supports making in educational administration

decision-One effective tool for plan making is spatial optimization, which can beimplemented in GIS (Drezner, 1996; Drezner and Hamacher, 2001) Spatialoptimization is a collection of mathematical techniques that derives thespatial structure of variables optimal in a certain aspect Imagine, forinstance, location planning of elementary schools in a new town There is

no existing school, and financial status permits opening two elementaryschools For simplicity, we assume that the geography of the town is homo-geneous and that the two schools provide the educational services of thesame quality In such a case, the distance from home to school is a critical

Trang 5

factor in location planning; the average distance from home to school should

be as small as possible Spatial optimization gives a set of such locations thatminimize the average distance from home to school

Spatial optimization can consider not only a single element of educationalenvironment, such as the distance from home to school, but also variousfactors simultaneously In locating schools in a region, the traffic condition

of the region, ethnic and racial balance among schools, the quality of teachersand programs also have to be taken into account Administrative system isalso an important element of educational administration These factors arerepresented as variables, either qualitative or quantitative, and incorporated

in mathematical calculations

Besides facility location, spatial optimization includes network planning,location, and allocation of resources, shortest-path finding, and so forth.Network-planning techniques are useful for discussing the route of schoolbuses, which is financially an important subject in educational administra-tion Location and allocation of educational resources, including teachersand facilities for education, can also be treated as a spatial-optimizationproblem

Once spatial-optimization techniques are implemented in GIS, we caninteractively compare alternatives for their decision-making (Lemberg andSmith, 1989; Ferland and Guénette, 1990; Armstrong et al., 1993; James, 1996).One may consider that the distance from home to school is very importantand derive the optimal location of schools that minimizes the average dis-tance from home to school Others may think that the ethnic balance amongschools is critical, which gives different optimal location of schools If spatial-optimization techniques are implemented in GIS, we can try various view-points of a problem to be solved, derive their optimal solutions, and comparethem using various measures

17.2.3 GIS for Evaluation in Educational-Administration Research

After a program is executed, whether it works successfully is of great interest

To evaluate an educational program, we again use methods of spatial ysis with those of policy evaluation

anal-Take, for instance, the charter-school program Unlike ordinary publicschools, charter schools are run by nonformal organizations consisting ofteachers, parents, and so forth, typically characterized by some unique edu-cational programs Charter schools don’t have a certain district but overlapwith those of ordinary schools, so that students can choose either a charter

or an ordinary school The main objective of the charter-school program is

to provide students alternatives to ordinary schools, which leads to a petition among schools, and, consequently, improves the quality and effi-ciency of education To evaluate the program, we need to know whether acharter school really draws students widely from its school district Com-paring the distributions of students of charter and ordinary schools using

com-2713_C017.fm Page 247 Thursday, September 22, 2005 9:07 AM

Trang 6

GIS, we can easily examine whether the students of the charter school aredistributed uniformly over its district, that is, whether the program worksefficiently

Similar to the charter-school program, the school-choice system also mits students to choose a school among several alternatives However, theschool-choice system aims not only to extend options for students but also

per-to obtain a desirable balance in ethnicity and race in an educational ronment, which is impossible in and ordinal school-district system Conse-quently, whether the school-choice system is successful should bedetermined by the ethnic and racial balance achieved by the program Tothis end, we compare the ethnic and racial compositions of individualschools and school districts using an overlay operation in GIS

envi-The school-bus system can also be evaluated efficiently in GIS It not only

is a safe transport system but also enables students to go to a school fromdistant places This allows large school districts, and, consequently, reduction

of schools for economic efficiency To evaluate the school-bus system, weneed to know whether students go to schools within a reasonable time Wecan easily do this using network analysis in GIS if we have spatial data oftraffic condition and bus routes

17.3 GIS for School Redistricting

As discussed in the previous section, GIS has a great potential of contribution

to educational-administration research To illustrate this concretely, thispaper presents an application of GIS to school redistricting After generaldiscussion in this section, an illustrative example is shown in the next section

17.3.1 School Districting in Elementary and Lower-Secondary Education

Elementary and lower-secondary education is compulsory in many tries To implement this, any student is assigned to one elementary and onesecondary school Though the school-choice system permits students tochoose one school from several alternatives, such a program is exceptional.Assignment of students to schools form a spatial structure called “schooldistricts.” In this paper, the term “school district” refers to the attendancearea in which students are assigned to a certain school by the local schoolboard, though “school district” often indicates the total area under the juris-diction of the school board

coun-School districting is based on various factors (Campbell and Cunningham,1990) Spatial factors include regional units, such as administrative units andcensus tracts, which reflect local communities The distance to the school isalso critical, especially in elementary education, where the school-bus system

Trang 7

is not adopted Young students should be assigned to nearby schools so thatthey do not have to walk so long to the schools In some cases, traffic network

is also considered; it is not desirable to cross roads of heavy traffic if studentswalk to school As well as these spatial factors, nonspatial factors are alsotaken into account in school districting, say, school capacity and politicalsocial problems Consequently, not all the school districts are based onadministrative units; some units overlap with more than one school districts

17.3.2 School Redistricting in Elementary and Lower-Secondary Education

In any country, school districts cannot be stable over time; they have tochange, inherently corresponding to the distribution of students In devel-oping countries, for instance, new schools are built continuously with anincrease of students This always involves school redistricting On the otherhand, school redistricting accompanies school closures in developed coun-tries, where students have been gradually decreasing To keep economicefficiency, schools of few students have to be shut down Old schools areoften closed because school buildings need rebuilding

School redistricting can occur without any change of schools When aschool-bus system is newly introduced, school districts are usually reexam-ined and changed School redistricting is often involved in adoption of anew educational program, such as the charter-school and school-choice sys-tem

Various factors have to be taken into account in school redistricting, aswell as in school districting In addition to spatial factors mentioned earlier,

it is important to keep the racial and ethnic balance in each school Variation

in educational programs among schools should be considered, because everyschool develops its own program in response to the local demand for edu-cation Consequently, school redistricting is a very complicated process ofdecision-making, which often takes considerable time

17.3.3 School-Family System

School districts are usually determined separately for elementary and secondary schools Consequently, one district of an elementary school mayoverlap with districts of more than one lower-secondary school (Figure17.2a) Students assigned to the same elementary school may go to differentlower-secondary schools

lower-Recently, however, a new system called school-family system has beenadvocated (Los Angeles Annenberg Metropolitan Project, 2004) In this sys-tem, one lower-secondary school and several elementary schools form a

school family Schools in the same family cooperate with each other in theeducation of students They share educational resources, such as teachersand school facilities, information of pupils and students, curriculum devel-opment, and teacher training In the United States, a school-family system

Trang 8

is introduced to improve the quality of teachers and the economic efficiency

of education

In the school-family system, each elementary-school district is fully tained in the district of one specific lower-secondary school (Figure 17.2b).Consequently, in a spatial aspect, school districts of the two education levelsshow a completely hierarchical structure, in other words, a tree-like struc-ture All the students assigned to the same elementary school go to the samelower-secondary school The school districts are determined simultaneously

con-17.3.4 School Redistricting as a Spatial-Optimization Problem

One approach to a school-redistricting problem is spatial optimization usingGIS (Garrison, 1959; Yeates, 1963; Heckman and Taylor, 1969; Bruno andAnderson, 1982; Greenleaf and Harrison, 1987; Schoepfe and Church, 1991;Lemberg and Church, 2000) In spatial optimization, objective function, vari-ables, and constraints are used to formalize the problem to be solved

An objective function is a quantitative measure of an alternative that wewant to maximize or minimize In elementary education, for instance, one

Trang 9

option is the average distance from home to school that should be minimized

in school redistricting On the other hand, if the racial and ethnic balance isimportant, the variance in ratios of different races and ethnicities can be theobjective function

A variable is a value that affects the objective function In school tricting, variables represent the parameters in alternatives that can be manip-ulated in planners and policy makers, such as assignment of students toschools, openings and closures of schools, and so forth

redis-A constraint represents the condition that has to be satisfied in the optimalsolution In optimization of school districts, it often happens that too manystudents are assigned to one school, while others have only a few students

To avoid such a case, we can impose conditions to an optimization problem,such as the minimum and maximum numbers of students at each school Ifsome schools have to be closed to improve economic efficiency, we may limitthe number of schools as a constraint In such a case, schools to be closedand student assignments are discussed simultaneously, that is, both factorsare included as variables in a spatial-optimization problem Formalizingconstraints as equations and inequalities, we solve a spatial-optimizationproblem to find values of the variables that minimize or maximize theobjective function satisfying the constraints

Figure 17.3 shows an example of a school-redistricting plan given by as aspatial optimization problem, where the average distance from home toschool is the objective function that should be minimized in school redis-tricting In this case, every student is assigned to the nearest school Conse-quently, as shown in Figure 17.3a, school districts form a Voronoi diagram,which is a spatial tessellation where every location is assigned to its nearestgenerator point (Okabe et al., 2000) We can see that the new districts areconsiderably different from the present ones where not all the students areassigned to the nearest schools If five schools are closed, school districts thatminimize the average distance from home to school are given by Figure17.3b Each district is almost twice as large as that in Figure 17.3a

17.4 School Redistricting in Kita Ward, Tokyo

This section presents an application of GIS to school redistricting in Japan,

in order to illustrate how the problem is resolved in the GIS environment.The focus is on the physical environment of elementary education ratherthan its qualitative aspects, since GIS is effective, especially for discussingspatial factors

In Japan, elementary and lower-secondary education is compulsory, andevery student is assigned to one elementary and one secondary school Assign-ment of students primarily depends on the administrative unit called cho-chomoku The area and population of one chochomoku in urban areas range

Trang 10

from 0.1 to 0.5 and 500 to 5000, respectively, while a wider variation exists inrural areas In principle, all the students in the same chochomoku are assigned

to one nearby elementary school Besides the distance to the school, trafficconditions are also considered To avoid being involved in traffic accidents,students should not cross major-traffic roads in going to school As well asthese spatial factors, as described earlier, qualitative factors are also taken intoaccount in determining school districts (for details, see Hayo, 1998)

17.4.1 Formulation of School-Redistricting Problem in Kita Ward, Tokyo

“Ward” is an administrative unit in Japan consisting of around 100 chomokus Kita Ward is located in the north of Tokyo Kita Ward’s area andpopulation in 2004 were 20.59 km 2 and 316,000, respectively Figure 17.4shows the districts of elementary schools in Kita Ward In this figure, wenotice that schools are usually located near the centers of school districts.This implies that many students are assigned to their nearest schools, thoughthere are some exceptions Figure 17.5 shows the districts of lower-secondaryschools in Kita Ward Compared with Figure 17.4, schools are not always

cho-FIGURE 17.3

Districts of elementary schools in Kita Ward, Tokyo.

(a) (b) Elementary school

New school districts Present school districts 2713_C017.fm Page 252 Thursday, September 22, 2005 9:07 AM

Định dạng
Số trang	21
Dung lượng	822,16 KB